ASSESSING GEOTECHNICAL CENTRIFUGE MODELLING IN …

B.R. Jones, L.B. Brouwers, W.D. Van Tonder, and M.A. Dippenaar 1

ASSESSING GEOTECHNICAL CENTRIFUGE MODELLING IN ADDRESSING VARIABLY

SATURATED FLOW IN SOIL AND FRACTURED ROCK

Brendon R. Jones*,1, Luke B. Brouwers1, Warren D. Van Tonder1, and Matthys A. Dippenaar1

1Engineering Geology and Hydrogeology, Department of Geology, University of Pretoria, Private Bag X20,

Hatfield, 0028, Pretoria, Gauteng, South Africa

*Corresponding author. Tel.: +27 (0)12 420 2454; e-mail address: [email protected]

ABSTRACT

The vadose zone typically comprises soil underlain by fractured rock. Often, surface water and groundwater

parameters are readily available, but variably saturated flow through soil and rock are oversimplified or

estimated as input for hydrological models. In this paper, a series of geotechnical centrifuge experiments are

conducted to contribute to the knowledge gaps in: (i) variably saturated flow and dispersion in soil; and (ii)

variably saturated flow in discrete vertical and horizontal fractures. Findings from the research show that the

hydraulic gradient and not the hydraulic conductivity is scaled for seepage flow in the geotechnical centrifuge.

Furthermore, geotechnical centrifuge modelling has been proved as a viable experimental tool for the modelling

of hydrodynamic dispersion as well as the replication of similar flow mechanisms for unsaturated fracture flow,

as previously observed in literature. Despite the imminent challenges of modelling variable saturation in the

vadose zone, the geotechnical centrifuge offers a powerful experimental tool to physically model and observe

variably saturated flow. This can be used to give valuable insight into mechanisms associated with solid-fluid

interaction problems under these conditions. Findings from future research can be used to validate current

numerical modelling techniques and address the subsequent influence on aquifer recharge and vulnerability,

contaminant transport, waste disposal, dam construction, slope stability and seepage into subsurface excavations.

Keywords: Unsaturated flow; fracture flow; dispersion; hydraulic conductivity; flow mechanism; smooth

parallel plate model.


1. INTRODUCTION

The implications of improved understanding of variably saturated flow through geologic media are numerous,

especially given the complexity, heterogeneity and anisotropy of the vadose zone. Worldwide surface

infrastructure is extending skywards as well as to greater depths below the surface. The increased need for

natural resources also implies deeper mines, larger dewatering cones around mines, dewatering of rock aquifers,

increased size and toxicity of waste disposal sites, and deep nuclear waste repositories. Prospects of deep

hydraulic fracturing (fracking) for shale gas or coal-bed methane raises questions about upward migration of

hydrocarbon liquids and gases, potentially rendering groundwater aquifers susceptible to contamination. These

anthropogenic activities impact on the hydrosphere and lithosphere and need to be quantified to determine

negative impacts and remedial measures. The quantification of water movement through rock masses also has

enormous economic implications. Water inflow into deep mines, building basements, underground tunnels

(water and transport), subsurface waste disposal sites (nuclear and other) and large rock caverns (hydro-electric

and storage facilities) needs to be quantified to create safe operational conditions.

In order to understand the specific influences of geologic media on variably saturated flow in the subsurface, one

needs to directly measure or observe the behaviour of fluids. To achieve this, physical modelling of fluid flow

through artificial or natural geologic media, simulated at a smaller laboratory scale, provides the best approach.

Physical models would allow one to directly measure or observe the influence that different properties will have

on fluid flow. If the model is proportionately scaled and one is aware of the assumptions made and the

implications on the modelling results, then the model may ultimately be regarded as a representative

simplification of the real system (Silberhorn-Hemminger et al. 2005). Small scale physical models are more

repeatable and less costly than large scale tests (Culligan-Hensley and Savvidou 1995). If the model is

considered to be representative, then the results will aid greatly to the understanding of fluid flow through

geologic media.

The research presented in this paper aims at assessing the geotechnical centrifuge in modelling and addressing

solid-fluid interaction problems associated with variable saturation in the vadose zone. Experimental work

described in this paper seeks to define some fundamental conceptual models. The aim is achieved by testing


some of these fundamental conceptual models associated with both soils and fractured rock, which involve

addressing the following set of objectives during the centrifuge modelling:

1. Revisiting the scaling issue of hydraulic conductivity or hydraulic gradient in the centrifuge at saturated

conditions;

2. Assessing the validity of transverse hydrodynamic dispersion in unsaturated conditions;

3. Investigating the validity in using the smooth parallel plate model in replicating unsaturated fracture

flow mechanisms.

Findings from the research address some issues as to whether it is plausible to observe or replicate recorded field

characteristics in a geotechnical centrifuge. The geotechnical centrifuge model tests were performed at various

scales using the 150 G-ton geotechnical centrifuge housed in the Department of Civil Engineering at the

University of Pretoria, of which the details of the centrifuge facility are described by Jacobsz et al. (2014).

2. LITERATURE

2.1 Variably saturated subsurface flow

Flow (seepage), wetting (imbibition) and drying (drainage) in unsaturated media becomes increasingly complex.

The potential for seepage in unsaturated conditions is driven by a combination of the gravitational potential and

the matrix potential (suction). The seepage through pores is largely dependent on the non-linear relationship

between suction, moisture content and hydraulic conductivity, which is unique to each soil sample (Nimmo

2006; Rumynin 2011). Literature on the topic is abundant and well documented internationally and in South

African context (e.g. Dippenaar 2012; Dippenaar 2014; Dippenaar et al. 2014).

In fractured media, seepage occurs both through the matrix and fractures where generally, the hydraulic

conductivity of the matrix is lower than the hydraulic conductivity of a fracture (Singhal and Gupta 2010).

However, flow in a fracture does not follow the same capillary-control as does flow in porous media, where

instead the hydraulic conductivity of fractures is dependent on the fracture aperture, roughness, infill, stress

conditions and geometrical properties (Berkowitz 2002). In natural conditions, fractures are both rough and

irregular but can be expressed by a simple model concept of two smooth parallel plates. Literature is abundant


on the topics of the smooth parallel plate model and the associated cubic law topics (e.g. Bear 1972; Berkowitz

2002; Dippenaar and Van Rooy 2016; Gudmundsson et al. 2003; Hoek and Bray 1981; Indraratna and Ranjith

2001; Liu et al. 2013; Neuman 2005; Silberhorn-Hemminger et al. 2005; Singhal and Gupta 2010; Weiss et al.

2006; Witherspoon et al. 1980; Zimmerman and Bodvarsson 1996). Importantly, Singhal and Gupta (2010) state

that the assumptions of the cubic law usually do not hold well in natural conditions, with the validity of cubic

law discussed by several researchers (Aydin 2001; Cook 1992; Dippenaar and Van Rooy 2016; Lee and Farmer

1993; Pyrak et al. 1985; Raven and Gale 1985; Sisavath et al. 2003; Witherspoon 1986).

Several flow mechanisms have been observed to occur in fractures at unsaturated conditions, as observed in flow

visualization experiments and conceptual modelling studies. Ghezzehei (2004) states that for an idealized

smooth fracture surface the most important mechanisms are; film flow, rivulet flow, and sliding of droplets.

Film flow (as presented by e.g.: Or and Tuller 2000; Tokunaga and Wan 1997; Tokunaga and Wan 2001) occurs

as thin films of water flowing along the fracture surface without having to fully saturate the fracture, and can

occur over a wide range conditions within unsaturated rocks. The thickness of the film depends on the degree of

saturation, where an increase in saturation results in thicker films. Droplet or liquid bridge flow can occur, as

hypothesised by Doe (2001), and echoed by Or and Ghezzehei (2007), whereby fluid spans both walls of the

fracture or drops that occur separately on adjacent walls within a fracture. An additional flow mechanism is that

of rivulets, of which there are three possible scenarios, as initially presented by Su et al. (1999) and further by

Dragila and Weisbrod (2003). The three scenarios are dependent on flow rates, whereby: at low flow rates

continuously snapping rivulets form liquid bridges within the fracture; at medium flow rates rivulets form and

only snap at the fracture’s end; and at high flow rates were rivulets that form are maintained throughout the

fracture. Although Doe (2001) presented that it is the wettability of the material that separates film and droplet

flow, recent research shows that different flow mechanisms can occur in fractures as presented by Dragila et al.

(2016) who showed the co-existence of droplets and film flow in vertical epikarst microfractures. Ghezzehei

(2004) showed how differing flow mechanisms can also occur over a wide range of contact angles, and fluxes.

Furthermore, the formation of these flow mechanisms is dependent on various factors, including the force

interactions between gravity, surface tension, capillary pressure, and viscous forces, which can result in complex

flow phenomena, such as episodic fluxes, intermittent fluxes and preferential flow paths (Dragila and Weisbrod

2003; Hakami and Larsson 1996; Su et al. 1999).


2.2 Geotechnical centrifuge modelling

A geotechnical centrifuge offers a powerful physical modelling technique that is capable of replicating

gravitational dependent processes between a scaled model and prototype conditions (Phillips 1995; Taylor 1995).

This is done by accelerating a model an equivalent N times Earth’s gravitational field g (ca. 9.81 m/s2) and

results in the model being subjected to a centrifugal acceleration Ng. The fundamental requirement for the

model and prototype to be similar is that the dimensionless groups are identical and similitude is achieved. A

plethora of appropriate scaling laws are used for centrifuge modelling, including: linear dimensions; stress; time;

Darcy’s Law; and Reynolds Number, which have been discussed in detail by Butterfield (2000), Culligan-

Hensley and Savvidou (1995), Kumar (2007), Taylor (1995), Phillips (1995) and Garnier et al. (2007).

2.2.1 Hydraulic conductivity and contaminant transport modelling

Conventional methods used to measure the hydraulic properties of soils rely on gravitational acceleration or an

applied pressure gradient to drive flow through a sample. Such methods are often time consuming, tedious and

limited to a small range of measurable hydraulic conductivity (K) values (Šimůnek and Nimmo 2005). However,

use of a geotechnical centrifuge allows for simple flow apparatus, decreased experimental time, larger range of

measurable K values, and the ability to simulate overburden pressure largely due to the development of the

steady state centrifuge method (Barry et al. 2001; Basha and Mina 1999; Nimmo 1990; Nimmo et al. 1992;

Nimmo and Mello 1991; Nimmo et al. 1987; Šimůnek and Nimmo 2005; Singh and Gupta 2000; Zornberg and

McCartney 2010). In terms of physical modelling of contaminant transport, the geotechnical centrifuge offers an

opportunity to bridge laboratory and field experiments by overcoming the limitations of these methods by being

able to model complex problems under repeatable conditions using large sample sizes, and better control of

experimental boundary conditions, while maintaining the ability to perform in flight monitoring (Mattson et al.

2010)

In determining the dispersion scaling factor, the mechanical dispersion coefficient cannot be considered a

material property because it is a function of both interstitial velocity and pore size (Culligan-Hensley and

Savvidou 1995). However, Hensley and Randolph (1994) investigated dispersion in a geotechnical centrifuge,

with results indicating that there is a scaling error for dispersion. The authors critically evaluated the derivation


of the scaling factor for dispersion and concluded that it is still possible to relate concentration distributions

using a scaling factor ranging between N and N1/2 for dispersion.

The above discussion deals with a well-established knowledge of miscible flow in a geotechnical centrifuge.

However, modelling of immiscible fluid flow in the geotechnical centrifuge is less prevalent and is mainly in the

form of experiments investigating Non-Aqueous Phase Liquids (NAPL) movement. Culligan and Barry (1998)

show that in order for similitude, the appropriate scaling factors, for the Capillary number, Bond number and

Stokes number (dimensionless parameters calculated by topical textbooks, including for e.g.; Poehls and Smith

2011) are dependent on whether the characteristic length of the system being investigated is macroscopic or

microscopic. In scenarios where the characteristic length is macroscopic, the appropriate scaling factors for the

Capillary and Bond number are constant, resulting in the similitude between the model and the prototype.

However, if the characteristic length is microscopic (i.e. pore throat size, fracture aperture), then the Capillary

and Bond should both be scaled by a factor of N, which may result in failure of geometric or kinematic

similitude elsewhere. Despite this violation of similitude, Culligan and Barry (1998) suggest that it is still

possible to use the geotechnical centrifuge in performing parametric experiments on immiscible fluid flow.

2.2.2 Modelling of flow through rock

Modelling of soil behaviour in the geotechnical centrifuge is well studied with a large amount of studies

available. Unfortunately, the same cannot be said for centrifuge modelling of rock masses, with literature limited

to geotechnical problems of rock slopes or mining instabilities (e.g. Cecconi et al. 2006; Chen et al. 2006;

Chikatamarla et al. 2006; Einstein et al. 1990; Günzel and Davies 2006; Itoh et al. 2006; Joseph and Einstein

1988; Li et al. 2014; Stone et al. 2013). This is due to the inability of using the prototype material in the model

due to the discontinuous nature of a rock mass and the lack of suitable analogue material alternative (Chen et al.

2006). Adopting the reasoning of Culligan and Barry (1998) for the problem of fracture flow, the ratio of body

gravity to capillary forces must be correct in order to simulate fluid invasion in a fracture, and therefore the

fracture aperture does not scale. Once fluid is in the fracture, similitude will depend on the flow mechanisms

themselves. Adopting fractures as microscopic lengths from the reasoning of Culligan and Barry (1998), Levy

et al. (2002) investigated dense-NAPL invasion into a fracture. The authors concluded that there is good

agreement between scaled centrifuge data and prototype data provided that inertial forces in the fracture remain


negligible. From these findings, Levy et al. (2003) formulated an equation to quantify the influence of inertial

forces by three regime criterion, in addition to the scaling laws proposed by Culligan and Barry (1998). Beyond

the discussed modelling of rock slope stability problems, and dense-NAPL experiments, no literature exists

relating to the modelling of unsaturated fracture flow in the geotechnical centrifuge.

3. MATERIALS AND METHODS

A series of centrifuge experiments evaluating some fundamental conceptual models of subsurface flow in both

soil and rock are developed:

• Experiment 1 attempts to verify scaling laws of seepage flow in a geotechnical centrifuge. Unlike the

subsequent experiments, this test was conducted in saturated conditions and sought to address the

uncertainties in scaling of hydraulic conductivity or hydraulic gradient in the centrifuge. It was

paramount to address this issue before attempting to address unsaturated conditions

• Experiment 2 expands on the first experiment and addresses the effect an increased gravitational

acceleration level has on transverse hydrodynamic dispersion under unsaturated conditions, and

whether the centrifuge is a viable tool in modelling dispersion problems.

• Experiment 3 examines the fundamental conceptual model of a clean smooth parallel plate for a

discrete fracture at vertical and horizontal orientations. Due to the novelty of unsaturated fracture flow

in the centrifuge, it is vital to first validate the fundamental conceptual models and whether similar flow

mechanisms presented in literature occur. Therefore, to emulate a smooth clean parallel plate model in a

centrifuge, acrylic Plexiglas sheets are selected due to the transparency and machinability of the

material.

4. EXPERIMENT 1: 1-DIMENSIONAL VERTICAL FLOW THROUGH SOIL

4.1 Model preparation and test procedure

The model developed by Van Tonder (2016), shown in Figure 1, is used to determine the permeability of a soil

sequence in a centrifuge and entails a 1000 mm tall acrylic Plexiglas cylinder with an inner diameter of 140 mm

placed inside an aluminium strongbox. The uniform fine-grained sand has an average particle size of 135 µm and


average reported permeability of 1.8 x 10-4 m/s to limit the number of variables (Archer 2014). The sand is

placed in de-aired water to a height of 600 mm above a 50 mm base filter. Three pore pressure transducers

(PPTs) are spaced at 200 mm intervals in the soil, with the bottom PPT placed above the filter and the top PPT

placed 200 mm below the soil surface. Solenoid valves (electronic tap) are connected to waste water outlet pipes

at the base of the model to control the hydraulic conductivity experiment procedure.

Figure 1. Test configuration for experiment 1: Modelling hydraulic conductivity or hydraulic gradient

The geotechnical centrifuge is accelerated to 23g, where consolidation is allowed to occur to obtain constant

pore water pressures. The initial water level (h1) is recorded and the solenoid valves is opened to initiate flow

through the model. To determine steady state flow, the pore pressures are monitored in-flight for a linear reading.


After the water level had dropped sufficiently, the solenoid valves are closed and the final water level (h2) is

recorded. The pore pressures are allowed to stabilise again before repeating the same procedure. Once the

centrifuge is stopped, the sample thickness and final water level are recorded before immediately filling the

cylinder with de-aired water to conduct a 1g experiment. The initial water level is again recorded before opening

the solenoid valves, where the water level is then allowed to fall to the same final level recorded in the 23g

experiment before the solenoid valves are closed and the test completed.

4.2 Results and discussion

The recorded physical observations from Van Tonder (2016) for both the 23g and 1g tests are presented in Table

1, where a total settlement of 4 mm (92 mm at prototype scale) occurs. During the first run of the 23g

experiment, the head dropped 0.14 m (3.22 m) in 139 seconds (20.42 hours), while an additional 0.097 m (1.94

m) head fell in 82 seconds (12.05 hours) during the second run, resulting in a total fall in head of 0.237 m (5.45

m) in 222 seconds (32 hours). For the 1g test, a fall of head of 0.24 m occurs significantly slower at 1911

seconds.

Table 1. The recorded physical observations at 1g and 23g.

Test h1 (m) h2 (m) Time (sec) Initial Sample Thickness (m)

Final Sample Thickness (m)

23g 1st Run 0.89 0.75 139 0.594 0.59 23 g 2nd Run 0.75 0.65 82 1g 0.90 0.66 1911 0.59 0.59

4.2.1 Pore pressures

The pore pressures for the 23g and 1g experiments are shown by Figure 2a and Figure 2b, respectively. For both

experiments, all the PPTs rapidly drop after the solenoid valves are opened and then decrease at a constant rate

during steady state flow before rapidly stabilising to new pore pressure values once the solenoid valves are

closed. Furthermore, PPT 1 experienced the maximum pore pressures when the solenoid valves are closed and

the greatest drop in pressure when the solenoid valves are opened, while PPT 2 records intermediary pore

pressures and pressure drops and PPT3 records the lowest pore pressures and pressure drops.


Figure 2. a) Recorded pore pressure data at 23g, and b) Recorded pore pressure data at 1g.

In the 23g test, the change in total head (ΔH) between each PPT in the model is extracted from the pore pressure

values and presented in

Table 2. A maximum ΔH is calculated between PPT 3 and PPT 1, while the minimum ΔH is calculated between

PPT 1 and PPT 2, indicating that the ΔH increases with increasing PPT separation distances.

Table 2. Calculated change in total head between each PPT at 23g.

PPT Elevation (m)

Hydrostatic conditions Steady state flow established ΔH

(kPa) hps (kPa) H (kPa) hz (kPa) hpf (kPa) Hf (kPa) hz (kPa)

3 0.4 85 163.4 78.36 67.8 146.16 78.36 26.06 2 0.2 127.1 163.4 36.34 95.2 131.54 36.34 14.62 1 0 163.4 163.4 0 120.1 120.1 0 11.40


In the 1g test, determining the ΔH between each PPT as shown in Table 3, required converting each PPTs pore

pressures during steady state flow in Figure 2b to pressure heads through the division by the unit weight of water

and adding the respective PPT elevation. The maximum ΔH again occurred between PPT 1 and 3, further

illustrating that ΔH increases correspondingly with PPT separation. However, the calculated ΔH for both the

lower and middle portions of the model are very similar and only differ by 0.0082 m, with the lower portion of

the model exhibiting a slightly larger ΔH and therefore showing that the ΔH decreases slightly with elevation.

Table 3. Calculated change in total head for each PPT at 1g.

PPT Elevation (m) Steady state flow established

hpf (kPa) Hpf (m) Hf (m) hpz (m) ΔH (m)

3 0.4 1.81 0.1845 0.5845 0.4 0.2756 2 0.2 2.46 0.2508 0.4508 0.2 0.1337 1 0 3.03 0.3089 0.3089 0 0.1419

When analysing the pore pressure data of both the 23g and 1g tests it becomes apparent that the pore pressures

display a similar distribution in both tests. It should be noted that the pore pressures in the 1g test provide lower

values due to the lack of centrifugal force to drive flow, while for the 23g test the increased acceleration

represents a prototype sample height of 11.4 m and the corresponding pore pressure values. Regardless of the

centrifugal force, all three PPTs respond rapidly in both tests with sharp pore pressures drops, indicating that the

model is hydraulically well connected, most likely related to the model’s hydraulic conductivity since fine-

grained sand is used in the model.

To assess the accuracy of the measured hydrostatic pore pressures in both the 23g and 1g tests, theoretical

hydrostatic pressure heads are calculated and plotted according to the respective PPT elevations within the

model, which indicate that initial hydrostatic head (hps ) increases with depth and correlate well with theoretical

distributions as shown in Figure 3a and Figure 3c. This accuracy is further supported by the total initial head (Hs),

which is constant throughout the column for both the 23g and 1g tests as shown in Figure 3b and Figure 3d, and

therefore means that measured pore pressure values are accurate.


Figure 3. Distribution of a) the calculated theoretical hps, measured hps and hpf, and b) Hs and Hf at 23g. Distribution of c) the calculated theoretical hps, measured hps and hpf, and d) Hs and Hf at 1g.

However, for both the 23g and 1g tests, the final hydrostatic head (hpf) increases with depth once flow is initiated,

with the maximum and minimum values still at PPT 1 and 3, respectively. This measured response does not

correlate to the expected theoretical response where the pore pressure at PPT 1 should decrease to atmospheric

pressure when the solenoid valves are open, and indicate that the tests are not free draining and therefore not a

true falling head test. This is due to the valves being flow constrictors, which caused the subsequent

accumulation of pore pressures through length of the sample. Despite the constriction posed by the outlet valves,

the final head (Hf ) for both the 23g and 1g tests decreases with depth and correlates to the expected theoretical

response as shown in Figure 3b and Figure 3d. Therefore, Bernoulli’s law is satisfied and downward flow is

maintained through the column.

4.2.2 Model hydraulic conductivity

The volumetric discharge (Q) is calculated for each test and together with the calculated ΔH, the K values

between each PPT for both acceleration levels are determined and presented in Table 4. The calculated average

K values for both the 23g and 1g test fall within the same order of magnitude. This indicates that the applied

inertial acceleration in the centrifuge has a minimal effect of compression of the material at high accelerations.


There are some differences between the K values calculated for the two tests, whereby the K value decreases

with elevation for the 23g test (PPT 1 to 2, and PPT 2 to 3), while the K value increases with elevation for the 1g

test (PPT 1 to 2, and PPT 2 and 3).

Table 4. Calculated difference in K-values (m/s) between the 23g and 1g tests. PPT K23g K1g K1g / K23g

1 to 2 1.716E-04 1.822E-04 1.062 2 to 3 1.343E-04 1.933E-04 1.440 1 to 3 1.507E-04 1.876E-04 1.245

Average 1.522E-04 1.877E-04 1.233

The calculated hydraulic conductivity calculated using the pore pressures for both the 23g and 1g tests falls

within the typical range of 1.00 x 10-5 m/s and 1.00 x 10-3 m/s for a fine-grained sand (Fetter 2001; Knappett and

Craig 2012), thereby providing a promising and accurate estimate of hydraulic conductivity. When comparing

the time taken for the head to fall by 0.24 m in each test, it is apparent that the 23g test took significantly less

time than the 1g test. This results in seepage velocity that is substantially larger in the centrifuge with hydraulic

conductivity scaling by a factor of N as concluded by Singh and Gupta (2002). However, the hydraulic

conductivities calculated using the measured pore pressures at 1g and 23g only differ by the small margins, as

shown in Table 4, where the 1g hydraulic conductivity is only 1.233 times greater than that of the 23g and can be

attributed to a slight densification of the sample in the centrifuge, which lowers the conductivity in the centrifuge.

Nevertheless, the measured difference is insignificant in terms of seepage and contradicts Singh and Gupta

(2002). This is further supported by the hydrostatic pore pressures (hps) of the 1g and 23g tests, where dividing

hydrostatic pore pressure of the 23g test with the average centrifugal acceleration provides almost identical

pressures compared to the 1g test as shown in Table 5.

Table 5. Comparison of the measured hydrostatic pore pressures at 1g and 23g

PPT Elevation (m) hps at 1g (kPa) hps at 23g (kPa) Hps at 23g / Nr (kPa) 1 0 8.732 163.4 8.600 2 0.2 6.485 127.1 6.689 3 0.4 4.804 85 4.474

The results from this experiment demonstrate that the calculated hydraulic conductivities for the 1g and 23g tests

and the reported hydraulic conductivities are in close accordance, proving (as mentioned by Robinson 2002) that

hydraulic conductivity is a material parameter that is unaltered in the centrifuge, assuming that the material does

not compress. A Reynolds number of 2.249 x 10-3 is calculated for the 23 g test, indicating that laminar flow

conditions prevailed during centrifugation, hence Darcy’s law is valid in the experiment. Therefore, in order to


scale seepage velocity appropriately, the hydraulic gradient must be scaled by a factor of N and not hydraulic

conductivity.

5. EXPERIMENT 2: UNSATURATED TRANSVERSE HYDRODYNAMIC DISPERSION


The model shown in Figure 4 is used to explore hydrodynamic dispersion in a geotechnical centrifuge. This

model is constructed in a strongbox with a window, where an inner-spacer plate is placed inside to reduce the

total base area to 150 x 600 mm. A 5 x 5 mm grid is placed against the window and identical dry sand used in

hydraulic conductivity model is pluviated from a height of 0.75 m to ensure a constant density range between

1600 kg/m3 and 1700 kg/m3. A small container with a 2 mm wide slit down the centre is lined with a geotextile

and placed in the centre, on top of the soil profile where it is connected to an inlet pipe leading from 4 l water

storage tank with a solenoid valve and an outlet pipe is installed in the base of the model.

Figure 4. Test set-up for experiment 2: Hydrodynamic dispersion.

Six tests are performed at acceleration levels of 1g, 2g, 5g, 10g, 20g and 40g respectively. In each test the

solenoid valve is opened and the storage tank is allowed to drain freely through the soil profile. The dispersion

plume evolution is visually captured by time interval photographs and the total extent of hydrodynamic


dispersion is recorded against the grid at reference depths of 50 mm, 100 mm and 150 mm below the soil surface

from the centreline to the right hand side of the model.


A summary of the results is provided in Table 6, accompanied by Figure 5, depicting the visual progression of

the plume in each test, at different stages of development. A number of assumptions are imposed on the results,

which include: (i) the soil is homogeneous and isotropic; (ii) the water properties are not affected by the addition

of food colourant; (iii) laminar flow conditions occur throughout the experiment; (iv) no rotational effects occur;

(v) and the principle axes of velocity and gravitational acceleration coincide resulting in transverse

hydrodynamic dispersion occurring perpendicular to this axes.

Table 6. Summary of transverse hydrodynamic dispersion experiments

g-level

Weight before (kg)

Weight after (kg)

Height of soil (mm)

Density (kg/m3)

Dispersion distance at reference depth (mm)

50mm 100mm 150mm 1 231.0 263.0 210 1693.12 170 145 90 2 232.0 263.0 210 1640.21 120* 110* 70* 5 232.0 261.0 200 1611.11 150* 140* 110*

10 232.0 262.0 200 1666.67 110 120 120 20 232.0 261.0 200 1611.11 50 65 75 40 233.0 263.0 200 1666.67 50 55 60

*Asymmetrical dispersion plume

In addition to these assumptions, a boundary error occurred in the 40g experiment where a water release problem

resulted in two dispersion plumes forming in the model. However, the results do not seem to be compromised, as

there is minimal interference between the two plumes allowing the dispersion readings to still be recorded.


Figure 5. Photographic sequence of the dispersion tests (5 mm x 5 mm grid). Value sin parenthesis refer to prototype time.

5.2.1 Dispersion plume evolution

At the start of each experiment, the dispersion plume expands in a circular fashion as the flow paths are forced to

flow around the soil grains. From this initial stage, depending on the level of gravitational acceleration, four

different plume progression and shape scenarios occur as shown in Figure 6, and are described as follows:

• Scenario 1: The plume continues to expand in a circular fashion in an attempt to saturate as much of the

soil as possible, resulting in a ever increasing semi-circular wetting front. This indicates that lateral

movement in the soil is the dominant direction of flow until a fully saturated column is formed and

downward progression occurs.


• Scenario 2: Evident in the 2g and to a lesser extent in the 5g experiments, is the progression of the

plume in an asymmetrical shape. This progression occurs due to the resultant acceleration level not

acting perpendicularly downwards from the soil surface but rather at an angle dependent on the

direction and magnitude of the two gravitational acceleration components. This provides results that are

unreliable, however, experiments performed at such low acceleration levels are impractical as upon

scaling of model dimensions, prototype conditions of 1 m will be modelled. Therefore, experiments

regarding seepage problems in a geotechnical centrifuge should be conducted at gravitational

acceleration levels of 10g or higher.

• Scenario 3: Occurs approximately between acceleration levels of 10g and 20g, and is the progression of

the dispersion plume with a reduced semi-circular wetting front. Initially the plume begins to disperse,

but is then forced to maintain its shape as it progresses through soil until contacting the bottom

boundary, where a boundary effect causes the fluid to pond and spread laterally, resulting in a final

shape of a bell.

• Scenario 4: Occurs at higher accelerations and is the progression of the plume as a saturated column

with a semi-circular end. The higher acceleration levels inhibit transverse dispersion as evident from the

maintained fixed shape during progression through the soil, which result ultimately in a column shape

as seepage occurs fast enough to stop spreading at the boundary.

Figure 6. Scenarios of plume shape.

5.2.2 Dispersion measurements

The final transverse dispersion readings at reference depths of 50 mm, 100 mm and 150 mm are represented by

the blue, red and green lines respectively in Figure 7, where the results for the 2g test have been omitted due to

the resultant gravitational force providing unreliable results.


Figure 7. Combined fine-grained reference depths dispersion distances at different acceleration levels At low gravitational acceleration levels (i.e. below 10g), there is a large range of dispersion values, with the

largest value occurring at shallower depths. This implies that at low gravitational acceleration levels, diffusion

briefly dominates the driving force until a saturation fringe is developed and the gravitational force then

dominates. Increasing the gravitational acceleration levels results in the dispersion distances converging to a

range of 115 to 120 mm during the 10g experiment, with the lowest value now occurring at the shallowest depth.

The increased gravitational acceleration level inhibits lateral dispersion and forces the dispersion plume

progression as a fixed shape within the soil profile.

Increasing the gravitational acceleration levels further maintains a fixed shape but causes a further reduction in

dispersion distances, which now range between 50 and 75 mm for the 20g experiment. Further increasing the

gravitational acceleration levels results in only a slight decrease in the dispersion distance, which now range

between 50 and 65 mm for the 40g experiment. This indicates that at approximately 20g acceleration levels, a

threshold dispersion distance ranging between 50 and 70 mm is obtained and no further decrease in dispersion

readings will occur with any further increase in gravitational acceleration levels.

5.2.3 Prototype conditions


To evaluate the validity of scaling dispersion in a geotechnical centrifuge, the reference depths are scaled using a

factor of 1:N and the dispersion distances for each of the respective reference depths are scaled using scaling

factor of 1:N, 1:N 0.9, 1:N0.8, 1:N0.75 and 1:N0.5 as proposed by Hensley and Randolph (1994). A scaling factor of

1:N produces the most amount of scatter in the data and results in large increases in dispersion distances with

increased prototype depths. This is unlike the 1:N0.5 scaling factor, which resulted in a lowest amount of scatter

in the data but contained the weakest correlation of all the scaling factors. However, using scaling factors

ranging between 1:N0.75 and 1:N0.9 provides data with a minimal degree of scatter while maintaining a

meaningful relationship between dispersion distance and prototype depth

Analysis of the scaled data revealed that a linear relationship exhibits low correlation and over-estimates

dispersion distances, while a polynomial and logarithmic relationship provides stronger correlation and better fit

for the data. Extrapolation of the polynomial relationship, shown in Figure 8a, indicates that with an increase in

the depth there is initially an increase in scaled dispersion distance followed by a rapid decrease until 10 m

prototype depth where zero dispersion occurs. This relationship indicates a scenario 3 plume and could represent

a scenario where a finite amount of fluid is added to the system or alternatively, an insufficient amount of time is

allowed to pass for the plume to migrate fully through the soil. Extrapolating the logarithmic relationship on the

other hand indicates an ever-increasing dispersion distance with depth and could possibly represent a steady state

flow with an infinite amount of source fluid scenario as shown in Figure 8b.


Figure 8. a) Semi-logarithmic graph of scaled prototype conditions with polynomial relationship, and b) Semi-logarithmic graph of scaled prototype conditions with logarithmic relationship.

To inspect if the calculated prototype conditions are a true representation of natural conditions, the dispersion

distances for the logarithmic relationship using scaling factors ranging between N0.75 to N0.9 is analysed and

provides a 30 m deep dispersion plume with a total plume width of 2.4 – 4 m. If the plume depth is regarded as


longitudinal dispersion and the plume width regarded as transverse dispersion, the ratio of transverse dispersion

(DT) and longitudinal dispersion (DL) range for these extrapolated values is shown in Equation 1.

!!"< %&

%'< !

(" Equation 1

This estimated ratio is approximately 1/10, which is the common ratio assumed between the two coefficients in

groundwater modelling (e.g. Aziz et al. 2000; Delleur 2006; Wiedemeier et al. 1996), indicating the geotechnical

centrifuge is viable experimental method to determine hydrodynamic dispersion.

6. EXPERIMENT 3: UNSATURATED DISCRETE FRACTURE FLOW


The vertical fracture model test is performed on a fracture measuring 100 mm height x 110 mm width, with a

constant aperture of 1 mm as shown in Figure 9a. Assuming saturated conditions and that the fracture aperture is

a microscopic length that does not scale, the fracture replica is therefore characterised by a hydraulic

conductivity (Kf) of 9.18 x 10-1 m/s. Model preparation begins with the placement of a camera and metal support

columns at the base of the model. Two bent L-section acrylic Plexiglas sheets measuring 299.5 mm long are

placed in a strongbox with a total length of 600 mm. This allowed a constant aperture of 1 mm to be maintained

for the fracture between the acrylic Plexiglas sheets. A back plate is then installed in the strongbox and three

screw jacks confine the fracture against the window and back plate where a water inlet container is constructed

around the fracture. Foam sealant tape is placed around the interior and exterior perimeter of the water inlet

container to maintain a watertight seal where potassium permanganate crystals are scattered to colour the water.

A water inlet pipe with a solenoid valve is installed above the fracture and an outlet is installed at the base of the

model.


Figure 9. Model set up for the: a) vertical fracture flow test (cross-sectional view is shown on the left, and side view - observing the vertical fracture perpendicularly- shown on the right); and b) horizontal fracture flow test (plan view - observing the horizontal fracture perpendicularly - shown on the top, and cross-sectional view shown on the bottom).


The horizontal fracture model test is performed on a horizontal fracture measuring 270 mm length x 110 mm

width, with a constant aperture of 1 mm, maintained by spacers. The hydraulic conductivity of the fracture is the

same as reported in the vertical experimental set-up. The model is constructed using the same two L-section

acrylic Plexiglas sheets, with one being slightly offset and inverted on top to allow for an inlet area as illustrated

in Figure 9b. A water inlet container is constructed over this area by jacking the back plate, while sealing the

interior and exterior perimeter with foam sealant to maintain a watertight seal, where potassium permanganate

crystals are scattered to colour the water. A camera is placed on an overhead bracket above the horizontal

fracture, while a second camera is placed on the right base of the model. A water inlet pipe with a solenoid valve

is installed above the container while an outlet pipe is installed at the base of the model.

The completed model is accelerated to 20g and tested under intermittent and continuous seepage conditions. For

intermittent seepage tests, the solenoid valve is opened and influx is introduced as individual droplets for 3

minutes (20 hours, at prototype scale) at approximately 0.6 l/hr, (12 l/hr). The centrifuge is then stopped, the

model dismantled, dried, and then reassembled for the continuous seepage test. The continuous seepage in the

fracture consists of opening the solenoid valve and allowing an initial influx of 20 l/hr (400 l/hr) into the model.

This is followed by 1-minute (6.67 hours) interval stepped influx increases, where an additional 20 l/h is added

to the current flux until a total constant flux of 100 l/h (2000 l/hr) is obtained for 1 minute. The water is then

closed and the system drains for an additional minute before repeating the same stepped flux procedure stated

above, but following shortened time intervals of 30 seconds (3.33 hours) between increases. The flow rate is

manually observed in the centrifuge control room by a flow meter. During high flow influx intervals (> 60 l/hr)

cavitation occurs in the inlet pipes, whereby flow ceases temporarily causing a backpressure in the pipes and

results in excess influxes being delivered to the model during re-stabilisation. Therefore, constant flow is not

always achieved at these intervals, and although all the influxes results are presented, the discussion generally

excludes the results of the intervals greater than 40 l/hr.


The following flow mechanisms were observed in the vertical fracture for both the intermittent and continuous

flow tests, and are presented in Figure 10:

A. Invasion of a 0.42 mm (8 mm) wide continuous rivulet, forming in approximately 0.1 seconds (40

seconds) through the length of the vertical fracture (Figure 10A-i to ii) over 90 mm (1.8m), during


initial introduction of water in the intermittent flow test. A discontinuous path of discrete sliding

droplets (Figure 10A-iii) forms adjacent to the initial rivulet, with an average width of 1 mm (20 mm)

and travel at approximately 150 mm/s (7.5 mm/s).

B. A continuous rivulet, which does not extend the entire length of the vertical fracture, and at a length of

approximately 20 mm becomes discontinuous where sliding droplets develop and detach intermittently.

In this instance, there is not a sufficient volume of water to establish a continuous rivulet, and therefore

discrete droplets break off from the rivulets when the weight of the drop is greater than the surface

tension, resulting in static droplets occurring within the fracture once the rivulet snaps.

C. Flow switching of continuous rivulets occur due to meandering rivulets that oscillate, which leads to

cessation of previous flow paths, and amalgamations with exiting flow paths, during the continuous

flow tests. The rivulets are approximately 0.5 to 1 mm (10-20 mm) wide and meander the entire length

of the fracture. Furthermore, the amalgamation during the flow switches are often dictated by the

position of static droplets scattered throughout the fracture.

D. Two populations of oscillating rivulets appear to cross-cut one another without influencing the observed

flow. This highlights that rivulets do not form spanning liquid bridges constrained between both

fracture walls but rather indicates flow occurs on opposing walls as continuous rivulets within the

fracture. This mechanism is further conceptualised in Figure 10D-iv; by a cross-sectional top-view

sketch through the vertical fracture.

E. Throughout the test intervals, preferential flow paths, with oscillating rivulets, give way to a curtain

flow at higher influxes (shaded portions in Figure 10E), but never fully saturates the width of the

fracture. At 20 l/hr (400 l/hr), the preferential flow paths formed by the continuous rivulets saturate

approximately 10% of the width of the fracture. This increases to 25% width area being saturated at 40

l/hr (800 l/hr); to 50% at 60 l/hr (1200 l/hr); and 70% at 80 l/hr (1600 l/hr), with full saturation not

being achieved at 100 l/hr (2000 l/hr).


Figure 10. Flow mechanisms observed in the vertical fracture (A: 5 mm x 5 mm grid; B to E: 10 mm x 10 mm grid).


The following observations are seen in the horizontal fracture, and the vertical outlet wall, for both the

intermittent (Figure 11) and continuous flow (Figure 12) tests:

• During the intermittent seepage test the wetting front is seen initially invading the horizontal fracture as

a circular wetting front as shown in Figure 11, which eventually contacts the spacer. This boundary

seems to act as a preferential flow path for the wetting front as it progresses through the fracture.

• In the intermittent test, approximately 60% of the fracture saturates before the first discrete sliding

droplet is noticed on the vertical wall at 112 seconds (12.4 hours, at prototype scale). Outflow along the

vertical wall continues to occur at the localised point of the initial breach by subsequent sliding droplets.

• Unlike the intermittent flow test, full saturation of the horizontal fracture occurs in the continuous flow

test in 0.71 seconds (4.7 minutes), as shown in the initial wetting phase in Figure 12.

• Upon saturation, a film of approximately 10 mm width (200 mm), is observed on the vertical wall with

an additional narrow oscillating rivulet (similar to flow mechanism C in the vertical fracture).

Increasing the influx to 40 l/hr widens the film to approximately 30 mm (600 mm), while maintaining

oscillation in the rivulet. Upon increasing the influx to 60 l/hr, the film widens to 50 mm (1000 mm),

and an additional 2 oscillating rivulets form. By 100 l/hr the width of the film is equivalent to the width

of the horizontal fracture. Throughout all intervals, the film at the vertical exit wall sweeps to the right.

• Upon rewetting, the capillary island that formed is mobilised, despite a small capillary island being

trapped at the edge of the exit of the horizontal fracture. The water exiting along the vertical face

follows the same flow mechanism as previously observed for all influx intervals.


Figure 11. Snapshot of the wetting front of the horizontal fracture for the intermittent (droplet) flow experiment (5 mm x 5 mm grid). The insert shows perspective for the reader (horizontal fracture and unconfined vertical outlet wall), as well as the sliding droplets on the unconfined vertical outlet wall.

The observed flow mechanism A, of the initial invading rivulet, is dissimilar to the mechanism observed at high

flow rates observed by Su et al. (1999), in that no prominent air-water meniscus (droplet) proceeds the rivulet.

Nevertheless, once established the rivulet is maintained throughout the fracture indicating a similar observation

to Su et al. (1999) for rivulets supplied by high flow rate. Furthermore, the discontinuous path of sliding

droplets that forms adjacent is also similar to the flow mechanism observed at low flow rates by Su et al. (1999),

and furthermore by results published by Ghezzehei and Or (2005). The presence of oscillating rivulets and flow

switches (flow mechanism C) indicate flow instabilities in unsaturated fractures, similar to the meandering

rivulets presented by Ghezzehei (2004). These flow instabilities are plausibly an indication that the flow through

an individual rivulet is approaching a maximum limit, for the specific contact angle and g level, specific to this

test. The observation of non-interacting intersections between meandering rivulets (flow mechanism D), as the

two populations of rivulets are flowing on the opposite sides of the fracture walls, is an important observation

indicating that the individual rivulets do not fill the fracture gap fully.


Figure 12. Screenshots of the horizontal fracture and vertical wall for the continuous flow experiment at each interval during the test, under 20G conditions (5mm x 5mm grid). The inserts show perspective for the reader (horizontal fracture and unconfined vertical outlet wall), as well as the resultant force acting on the film on the unconfined vertical outlet wall, causing it to sweep.


The observation of rivulets, and sliding droplet flow mechanisms, as well as film flow (only in the horizontal

experiment) is important. If one considers the phase diagram of Ghezzehei (2004), contact angles of 70° for the

acrylic Plexiglas used (e.g. Aouad et al. 2016; Della Volpe et al. 2002; Sumner et al. 2004) at the flow rates

tested, rivulets and sliding droplets should dominate the observed flow mechanisms. The observation of co-

existing droplet and rivulet flow mechanisms is likely a function of the test set-up, and not due to the same

process as presented by Dragila et al. (2016). In these instances, directly beneath the inlet pipe, there is lateral

accumulation of water above the fracture entrance. The continuous rivulet forms directly beneath the inlet pipe

and is supplied by the majority of water being introduced. Conversely, the intermittent rivulet is being supplied

by the rejected lateral accumulation of water above the fracture entrance, at a much lower flow rate. This

discontinuous path of intermittent sliding droplets observed in flow mechanism A, results from water ponding

above the fracture growing to some critical size, and forming a thinning neck that eventually snaps, releasing a

droplet from the top of the fracture. Similar reason can be used to explain flow mechanism B, whereby a

continuous rivulet terminates to a discontinuous path of intermittent sliding droplets. Here a reduced influx for

this particular feature, again from a lateral accumulation above the fracture entrance, results in an insufficient

quantity of water to establish a fully-continuous rivulet, and instead an intermittent rivulet forms releasing

sliding droplets when the weight of the droplet is greater than the surface tension.

The sweeping of the wide films at the vertical wall in the horizontal test is due to a resultant force, due to the

interaction between the centripetal force acting perpendicular to the centrifuge platform and gravity force acting

towards the centre of the Earth. This influence is only noted for these films with large volumetric fluxes and are

plausibly a function of the volume of water being transmitted. The path followed by the sliding droplets and

rivulets within the fracture can be attributed to the wetting capability of the material as described by Doe (2001),

whereby generally the same cross-sectional drainage area re-saturates during rewetting.

By treating the fracture width as a microscopic length (as discussed by Culligan and Barry 1998), the scaled

model results do not accurately represent natural conditions. In this instance, despite the similitude failure of the

Capillary and Bond numbers, the Stokes number, which describes gravity driven flow instability, remains

constant and suggests that the observed oscillating, meandering, flow switching and merging of rivulets within

the model does occur in natural conditions. The observation of similar flow mechanisms in the fracture in the

form of sliding droplets, rivulets is consistent with those published in literature. This signifies that although the


results from the geotechnical centrifuge model may not be scaled to prototype conditions, the observed flow

mechanisms and flow instabilities are representative of natural conditions.

This good accordance between flow mechanisms observed in a geotechnical centrifuge and previous research

indicates that the geotechnical centrifuge replicates variably saturated flow mechanisms acceptably. An

important issue observed in replicating the parallel plate conceptual model is that full saturation is never

achieved in any of the vertical fractures (as a required assumption of the cubic law as stated by e.g. Silberhorn-

Hemminger et al. 2005; Singhal and Gupta 2010; Zimmerman and Bodvarsson 1996), including that of the

vertical wall of the horizontal test where the horizontal fracture is fully saturated. However, considering that the

cubic law is an expression for fracture permeability, the flow that you would get through a saturated fracture

under the experimental conditions investigated is very likely to be much higher than the imposed flow rate, from

the inlet pipe. Furthermore, full saturation is not even achieved in the horizontal fracture during the intermittent

test. In a separate study being prepared, the authors (Jones et al. in review) present that a plausible explanation

could be in using the continuity principle whereby water should theoretically be transported downward at

significantly higher flow rates given the very low degree of water saturation in the vertical fractures compared to

horizontal fractures. A reduced rate of input, results in a smaller cross-sectional drainage area and appearance of

sliding droplets that form when the weight of the droplets, attached to the ponding of water in the horizontal

fracture, are greater than the surface tension of the vertical wall and are released. Therefore, a current prominent

challenge is understanding the interaction of film and capillary forces within a fracture, so that multiple flow

mechanisms and sporadic flow instabilities can be accurately described and quantified, in assessing flow through

more complex natural conditions of the intermediate fractured vadose zone. Despite the difficulties currently

being faced, understanding the complex flow regimes and force interactions is a current research area in

unsaturated fluid mechanics (e.g. Dragila and Weisbrod 2003; Ghezzehei 2004; Kordilla et al. 2013; Or and

Ghezzehei 2007; Su et al. 1999).

7. CONCLUSIONS

7.1 Limitations and lessons learnt


Research presented in this paper has only investigated homogenous fine sand. Although it was pertinent to

assess such fundamental concepts initially, the influence of anisotropy and heterogeneity which exists in the

subsurface cannot be ignored. The fracture flow research as discussed in this paper is limited to the smooth

parallel perfectly horizontal or vertical acrylic Plexiglas fracture with 1 mm aperture. In order to further validate

the geotechnical centrifuge as a viable tool of modelling rock masses, future research will need to show that it is

indeed possible to model the impact that fracture characteristics (as presented by Berkowitz 2002) such as

roughness and waviness has on how, rather than how much, flow occurs through discrete fractures under

conditions of variable saturation. Geometrical properties will likely become increasingly harder to model when

constructing a scaled-down centrifuge model, and therefore could compromise the accurate representation of the

contact areas, and the geometry of discrete fracture. In the same light, when considering the scale of fractures,

particularly at larger scales; there will be a threshold aperture were a fracture become macroscopic and not

microscopic, and potentially contest the reasoning of Culligan and Barry (1998).

7.2 Main findings

Findings from the research presented in this paper show that the hydraulic gradient and not the hydraulic

conductivity is scaled for seepage flow in the geotechnical centrifuge. Furthermore, geotechnical centrifuge

modelling has been proven as a viable experimental tool for the modelling of hydrodynamic dispersion as well

as the replication of similar flow mechanisms for unsaturated fracture flow, as previously observed in literature.

In these fundamental experimental models, despite full saturation being achieved for high flow rates in a

horizontal fracture, flow through the vertical fracture violates assumptions of the cubic law where full saturation

is never achieved and flow is neither uniform, nor laminar. If such an ideal model is unable to duplicate the

assumptions of the cubic law, its use in numerical models should be queried in the intermediate fractured vadose

zone.

Despite the imminent challenges of modelling variable saturation in the vadose zone, the geotechnical centrifuge

offers a powerful experimental tool to physically model and observe variably saturated flow. Although an exact

reproduction of unsaturated fracture flow is not likely achieved using the geotechnical centrifuge, it does have a

valuable role to play in delineating and understanding the physical mechanisms that control this complex

problem. This can be used to give valuable insight into mechanisms associated with solid-fluid interaction


problems under conditions of variable saturation. Findings from future research can be used to validate current

numerical modelling techniques and address the subsequent influence on aquifer recharge and vulnerability,

contaminant transport, waste disposal, dam construction, slope stability and seepage into subsurface excavations.

Oversimplification of the influence of the vadose zone through for instance: black box modelling; simplification

to basic primary porosity systems; consideration of only saturated hydraulic parameters; and the like, result in a

misrepresentation of the role of the vadose zone in hydrological systems. Most models may potentially fail due

to this lack of input. Further to this, the typical vadose zone comprising soil overlying fractured rock can be

better modelled with improved understanding of how these two media behave individually, but more importantly

in a combined sequence.

ACKNOWLEDGEMENTS

The authors wish to acknowledge the Water Research Commission of South Africa (www.wrc.org.za) for

funding of project K5/2052 on Multidisciplinary Vadose Zone Hydrology, as well as project K5/2326 on

Quantification of Unsaturated Flow in the Fractured Intermediate Vadose Zone by means of Geotechnical

Centrifuge (to be published by the WRC in 2016). Furthermore, acknowledgement is extended to Prof S.W.

Jacobsz and Prof J.L. Van Rooy for their guidance and input into this paper. Gratitude is also extended to the

National Research Foundation (NRF) as well as Exxaro Resources Ltd, for their financial assistance to some of

the authors of this paper. The authors declare no conflict of interest.

REFERENCES

Aouad W, Landel JR, Dalziel SB, Davidson JF, Wilson DI (2016) Particle image velocimetry and modelling of

horizontal coherent liquid jets impinging on and draining down a vertical wall Experimental Thermal

and Fluid Science 74:429-443 doi:http://dx.doi.org/10.1016/j.expthermflusci.2015.12.010

Archer A (2014) Using small-strain stiffness to predict the settlement of shallow foundations. Unpublished

MEng dissertation, Pretoria: University of Pretoria.[Links]

Aydin A (2001) Fracture void structure: implications for flow, transport and deformation Environmental

Geology : International Journal of Geosciences 40:672-677


Aziz C, Newell C, Gonzales J, Haas P, Clement T, Sun Y (2000) BIOCHLOR Natural Attenuation Decision

Support System. User’s Manual Version 1.0 US Environmental Protection Agency

Barry D, Lisle I, Li L, Prommer H, Parlange JY, Sander GC, Griffioen J (2001) Similitude applied to centrifugal

scaling of unsaturated flow Water Resources Research 37:2471-2479

Basha H, Mina N (1999) Estimation of the unsaturated hydraulic conductivity from the pressure distribution in a

centrifugal field Water resources research 35:469-477

Bear J (1972) Dynamics of fluids in porous media American Else-vier, New York

Berkowitz B (2002) Characterizing flow and transport in fractured geological media: A review Advances in

Water Resources 25:861-884 doi:http://dx.doi.org/10.1016/S0309-1708(02)00042-8

Butterfield R (2000) Scale-Modelling of Fluid Flow in Geotechnical Centrifuges Journal of the Japanese

Geotechnical Society: Soils and Foundation 40:39-45

Cecconi M, Croce P, Viggiani G Physical modelling of block toppling. In: Physical Modelling in Geotechnics,

Two Volume Set: Proceedings of the Sixth International Conference on Physical Modelling in

Geotechnics, 6th ICPMG'06, Hong Kong, 4-6 August 2006, 2006. CRC Press, p 325

Chen ZY, Zhang JH, Wang WX, Xing YC (2006) Centrifuge modelling of rock slopes. In: Ng CW, Wang Y-H,

Zhang L (eds) Physical Modelling in Geotechnics, Two Volume Set: Proceedings of the Sixth

International Conference on Physical Modelling in Geotechnics, 6th ICPMG'06, Hong Kong, 4-6

August 2006, vol 1. CRC Press, pp 19-28

Chikatamarla R, Laue J, Springman S Modelling of rockfall on protection galleries. In: 6th International

Conference on Physical Modelling in Geotechnics, 2006. pp 331-336

Cook N (1992) Natural joints in rock: Mechanical, hydraulic and seismic behaviour and properties under normal

stress International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts

29:198-223

Culligan P, Barry D (1998) Similitude requirements for modelling NAPL movement with a geotechnical

centrifuge Proc Instn Civ Engrs Geotech Engng:180-186

Culligan-Hensley PJ, Savvidou C (1995) Environmental geomechanics and transport processes In: Taylor R (ed)

Geotechnical centrifuge technology. CRC Press, pp 201-271

Della Volpe C, Maniglio D, Morra M, Siboni S (2002) The determination of a ‘stable-equilibrium’contact angle

on heterogeneous and rough surfaces Colloids and Surfaces A: Physicochemical and Engineering

Aspects 206:47-67


Delleur JW (2006) Elementary Groundwater Flow and Transport Processes In: Delleur JW (ed) The handbook of

groundwater engineering. CRC press, pp 3.1-3.45

Dippenaar MA (2012) How we lose ground when earth scientists become territorial: defining “soil” Natural

resources research 21:137-142

Dippenaar MA (2014) Porosity reviewed: quantitative multi-disciplinary understanding, recent advances and

applications in vadose zone hydrology Geotechnical and Geological Engineering 32:1-19

Dippenaar MA, Van Rooy JL (2016) On the cubic law and variably saturated flow through discrete open rough-

walled discontinuities International Journal of Rock Mechanics and Mining Sciences 89:200-211

doi:http://dx.doi.org/10.1016/j.ijrmms.2016.09.011

Dippenaar MA, van Rooy JL, Breedt N, Huisamen A, Muravha SE, Mahlangu S, Mulders JA (2014) Vadose

zone hydrology: Concepts and techniques. Water Research Commision (WRC), Pretoria

Doe TW (2001) What do drops do? Surface wetting and network geometry effects on vadose-zone fracture flow

Conceptual models of flow and transport in the fractured vadose zone:243-270

Dragila MI, Hay KM, Wheatcraft SW (2016) 9. Initial pipe development within epikarst microfractures

Geological Society of America Special Papers 516:129-136

Dragila MI, Weisbrod N (2003) Parameters affecting maximum fluid transport in large aperture fractures

Advances in Water Resources 26:1219-1228

Einstein HH, Li V, Whitman RV, Veneziano D, Reyes O, Iglesia G, Lee J-S (1990) Stochastic and Centrifuge

Modelling of Jointed Rock. DTIC Document,

Fetter C (2001) Applied hydrogeology, Fourth edn. Prentice-Hall, New Jersey

Garnier J et al. (2007) Catalogue of scaling laws and similitude questions in geotechnical centrifuge modelling

International Journal of Physical Modelling in Geotechnics 7:1

Ghezzehei TA (2004) Constraints for flow regimes on smooth fracture surfaces Water Resources Research

40:n/a-n/a doi:10.1029/2004WR003164

Ghezzehei TA, Or D (2005) Liquid fragmentation and intermittent flow regimes in unsaturated fractured media

Water resources research 41

Gudmundsson A, Gjesdal O, Brenner SL, Fjeldskaar I (2003) Effects of linking up of discontinuities on fracture

growth and groundwater transport Hydrogeology Journal 11:84-99 doi:10.1007/s10040-002-0238-0

Günzel F, Davies M Influence of warming permafrost on the stability of ice filled rock joints. In: Proceedings,

6th International Conference on Physical Modelling in Geotechnics, 2006. pp 343-348


Hakami E, Larsson E Aperture measurements and flow experiments on a single natural fracture. In: International

Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 1996. vol 4. Elsevier, pp

395-404

Hensley P, Randolph M Modelling contaminant dispersion in saturated sand. In: Proceedings of the international

conference on soil mechanics and foundation engineering-international society for soil mechanics and

foundation engineering, 1994. AA Balkema, pp 1557-1557

Hoek E, Bray J (1981) Rock slope engineering. Rev. 3rd ed. edn. Institution of Mining and Metallurgy, London :

Indraratna B, Ranjith P (2001) Hydromechanical aspects and unsaturated flow in jointed rock. A.A. Balkema

Publishers, Lisse [Netherlands] ;

Itoh K, Toyosawa Y, Kusakabe O, Ng C, Zhang L, Wang Y Centrifugal modelling of rockfalls. In: Proceedings

of the 6th International Conference on Physical Modelling in Geotechnics–ICPMG, Hong Kong (Ng

CWW, Zhang LM and Wang YH (eds)). Taylor & Francis, London, UK, 2006. pp 349-354

Jacobsz S, Kearsley E, Kock J The geotechnical centrifuge facility at the University of Pretoria. In:

ICPMG2014–Physical Modelling in Geotechnics: Proceedings of the 8th International Conference on

Physical Modelling in Geotechnics 2014 (ICPMG2014), Perth, Australia, 14-17 January 2014, 2014.

CRC Press, p 169

Jones BR, Brouwers LB, Dippenaar MA (in review) Initially dry vertical fractures fail to saturate under free-

draining conditions International Journal of Rock Mechanics and Mining Sciences Manuscript Number:

IJRMMS-S-16-00410

Joseph P, Einstein H (1988) Rock modeling using the centrifuge. DTIC Document,

Knappett J, Craig RF (2012) Craig's soil mechanics. Spon Press,

Kordilla J, Tartakovsky AM, Geyer T (2013) A smoothed particle hydrodynamics model for droplet and film

flow on smooth and rough fracture surfaces Advances in Water Resources 59:1-14

doi:http://dx.doi.org/10.1016/j.advwatres.2013.04.009

Kumar P (2007) Scaling laws and experimental modelling of contaminant transport mechanism through soils in

a geotechnical centrifuge Geotechnical and Geological Engineering 25:581-590

Lee C-H, Farmer IW (1993) Fluid flow in discontinuous rocks. 1st ed. edn. Chapman & Hall, London ;

Levy LC, Culligan PJ, Germaine JT (2002) Use of the geotechnical centrifuge as a tool to model dense

nonaqueous phase liquid migration in fractures Water resources research 38


Levy LC, Culligan PJ, Germaine JT (2003) Modelling of DNAPL behavior in vertical fractures International

Journal of Physical Modelling in Geotechnics 3:01-18

Li X, Wartman J, Tang H, Yan J, Luo H, Hu W (2014) Dynamic Centrifuge Modelling Tests for Sliding Rock

Slopes. In: Landslide Science for a Safer Geoenvironment. Springer, pp 75-79

Liu H-H, Wei M-Y, Rutqvist J (2013) Normal-stress dependence of fracture hydraulic properties including two-

phase flow properties Hydrogeology Journal : Official Journal of the International Association of

Hydrogeologists 21:371-382

Mattson ED, Palmer C, Smith RW, Flury M (2010) Centrifuge techniques and apparatus for transport

experiments in porous media vol 1. Taylor and Francis Group: London,

Neuman SP (2005) Trends, prospects and challenges in quantifying flow and transport through fractured rocks

Hydrogeology Journal 13:124-147

Nimmo JR (1990) Experimental Testing of Transient Unsaturated Flow Theory at Low Water Content in Water

Resources Research 26:1951-1960

Nimmo JR (2006) Unsaturated zone flow processes Encyclopedia of Hydrological Sciences

Nimmo JR, Akstin KC, Mello KA (1992) Improved apparatus for measuring hydraulic conductivity at low water

content Soil Science Society of America Journal 56:1758-1761

Nimmo JR, Mello KA (1991) Centrifugal techniques for measuring saturated hydraulic conductivity Water


Nimmo JR, Rubin J, Hammermeister D (1987) Unsaturated flow in a centrifugal field: Measurement of

hydraulic conductivity and testing of Darcy’s law Water Resour Res 23:124-134

Or D, Ghezzehei TA (2007) Traveling liquid bridges in unsaturated fractured porous media Transport in Porous

Media 68:129-151

Or D, Tuller M (2000) Flow in unsaturated fractured porous media: Hydraulic conductivity of rough surfaces

Water Resources Research 36:1165-1177

Phillips R (1995) Centrifuge modelling: practical considerations Geotechnical centrifuge technology:34-60

Poehls D, Smith GJ (2011) Encyclopedic dictionary of hydrogeology. Academic Press,

Pyrak LR, Myer LR, Cook NGW (1985) Determination of fracture void geometry and contact area at different

effective stress. Eos Trans AGU 66

Raven KG, Gale JE (1985) Water flow in a natural rock fracture as a function of stress and sample size

International Journal of Rock Mechanics and Mining Sciences 22:251-261


Robinson R (2002) Modelling hydraulic conductivity in a small centrifuge: Discussion Canadian Geotechnical

Journal 39:486-487

Rumynin VG (2011) Water Movement and Solute Transport in Unsaturated Porous Media. In: Subsurface

Solute Transport Models and Case Histories. Springer, pp 77-119

Silberhorn-Hemminger A, Süß M, Helmig R (2005) Natural fractured porous systems. In: Dietrich P, Helmig,

R., Sauter, M., Hӧtzl, H., Kӧngeter, J., and Teutsch, G. (ed) Flow and transport in fractured porous

media. . Springer, Berlin, pp 16-24

Šimůnek J, Nimmo JR (2005) Estimating soil hydraulic parameters from transient flow experiments in a

centrifuge using parameter optimization technique Water resources research 41

Singh DN, Gupta AK (2000) Modelling hydraulic conductivity in a small centrifuge Canadian Geotechnical

Journal 37:1150-1155

Singh DN, Gupta AK (2002) Modelling hydraulic conductivity in a small centrifuge: Reply Canadian

Geotechnical Journal 39:488-489

Singhal BBS, Gupta RP (2010) Applied hydrogeology of fractured rocks. 2nd ed. edn. Springer, Dordrecht ;

Sisavath S, Al-Yaaruby A, Pain CC, Zimmerman RW (2003) A Simple Model for Deviations from the Cubic

Law for a Fracture Undergoing Dilation or Closure Pure and Applied Geophysics 160:1009-1022

Stone KJL, Maquin M, Richards DJ, Montouchet M (2013) Physical and numerical modeling of problems in

homogeneous and fractured soft rock masses. In: ICPMG2014 Physical Modelling in Geotechnics.

CRC Press, pp 413-417. doi:10.1201/b16200-53

Su GW, Geller JT, Pruess K, Wen F (1999) Experimental studies of water seepage and intermittent flow in

unsaturated, rough-walled fractures Water Resources Research 35:1019-1037

Sumner AL et al. (2004) The nature of water on surfaces of laboratory systems and implications for

heterogeneous chemistry in the troposphere Physical Chemistry Chemical Physics 6:604-613

doi:10.1039/B308125G

Taylor R (1995) Centrifuges in modelling: Principles and scale effects. In: Taylor R (ed) Geotechnical centrifuge

technology. CRC Press, pp 20-34

Tokunaga TK, Wan J (1997) Water film flow along fracture surfaces of porous rock Water Resources Research

33:1287-1295

Tokunaga TK, Wan J (2001) Approximate boundaries between different flow regimes in fractured rocks Water



Van Tonder W (2016) Centrifuge Modelling of Permeability of a Heterogeneous Coal Mine Backfill Sequence.

Unpublished MSc Dissertation, University of Pretoria

Weiss M, Rubin Y, Adar E, Nativ R (2006) Fracture and bedding plane control on groundwater flow in a chalk

aquitard Hydrogeology Journal 14:1081-1093

Wiedemeier TH, Wilson JT, Hansen JE, Chapelle FH, Swanson MA (1996) Technical Protocol for Evaluating

Natural Attenuation of Chlorinated Solvents in Groundwater. Revision 1. DTIC Document,

Witherspoon PA (1986) Flow of groundwater in fractured rocks Bulletin of the International Association of

Engineering Geology 34:103-115

Witherspoon PA, Wang JSY, Iwai K, Gale JE (1980) Validity of Cubic Law for fluid flow in a deformable rock

fracture Water Resources Research 16:1016-1024

Zimmerman RW, Bodvarsson GS (1996) Hydraulic conductivity of rock fractures Transport in Porous Media

23:1-30

Zornberg JG, McCartney JS (2010) Centrifuge permeameter for unsaturated soils. I: Theoretical basis and

experimental developments Journal of Geotechnical and Geoenvironmental Engineering 136:1051-1063

ASSESSING GEOTECHNICAL CENTRIFUGE MODELLING IN …

Documents

Transcript of ASSESSING GEOTECHNICAL CENTRIFUGE MODELLING IN …